Test of hypothesis (two-tail)

We shall be testing hypotheses about the population mean (it is assumed we know the variance of the population). We shall fail to reject the hypotesis if the obseved sample mean (x-bar) is close to the hypothesized population mean (µ). We will shall reject the hypothesis if the observed sample mean (x-bar) is far from the hypothesized population mean (µ). Distance will be measured in standard deviation units (z-scores) based on the hypothesis being true, or the probability of the z-score being that large.

A test of hypotheis entails:

Example: If you are told that the mean weight of 3rd graders is 85 pounds with a standard deviation of 20 pounds, and you find that the mean weight of a group of 22 students is 95 pounds, do you question that that group of students is a group of third graders? N.B.: